Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#17984873 | C2 | semidirect |
| 2. C2×#17984868 | C2 | semidirect |
| 3. C2×#17984864 | C2 | semidirect |
| 4. #22581527 | C2 | semidirect |
| 5. #22581520 | C2 | semidirect |
| 6. #22581344 | C2 | semidirect |
| 7. #22581339 | C2 | semidirect |
| 8. #22581334 | C2 | semidirect |
| 9. #22581324 | C2 | semidirect |
| 10. #22580908 | C2 | semidirect |
| 11. C22×SD16×C139 | C2 | semidirect |
| 17. C2×Dic556 | C22 | semidirect |
| 18. C2×#14555775 | C22 | semidirect |
| 19. C2×#14555774 | C22 | semidirect |
| 20. C2×#14555774 | C22 | semidirect |
| 22. C2×#14555772 | C22 | semidirect |
| 23. C2×D1112 | C22 | semidirect |
| 26. #17984840 | C22 | semidirect |
| 28. #17984831 | C22 | semidirect |
| 35. #17984752 | C22 | semidirect |
| 36. C8×Dic139 | C22 | semidirect |
| 64. #14555769 | D4 | semidirect |
| 85. C2×C8×C139 | D4 | semidirect |
| 148. C139 | #3154 | semidirect |
| 153. C22×SD16 | D139 | semidirect |
| 228. C2×C8 | C22⋊D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984873 | 2 |
| C2×#17984868 | 2 |
| C2×#17984864 | 2 |
| #22581527 | 2 |
| #22581520 | 2 |
| #22581344 | 2 |
| #22581339 | 2 |
| #22581334 | 2 |
| #22581324 | 2 |
| #22580908 | 2 |
| C22×SD16×C139 | 2 |
| #3154 | 139 |